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Let's simplify the expression:

\[
\frac{8x^2y^2}{4x^2y^6}
\]

1. First, divide the coefficients:  
   \[
   \frac{8}{4} = 2
   \]

2. Now simplify the powers of \(x\). Since both numerator and denominator have \(x^2\), they cancel out:
   \[
   \frac{x^2}{x^2} = 1
   \]

3. Next, simplify the powers of \(y\). Using the rule \(y^a / y^b = y^{a-b}\), we get:
   \[
   \frac{y^2}{y^6} = y^{2-6} = y^{-4}
   \]

Therefore, the simplified expression is:

\[
2y^{-4} = \frac{2}{y^4}
\]

Let me know if you would like further details or have any questions!

Here are five related questions:
1. How do you simplify expressions with negative exponents?
2. What is the rule for dividing powers with the same base?
3. Can you simplify \(\frac{6x^3y^4}{3x^2y^2}\)?
4. How would you simplify \(\frac{10x^5}{2x^3y^2}\)?
5. What is the result of simplifying \(\frac{12a^3b^2}{6a^2b^4}\)?

**Tip:** When simplifying expressions with exponents, always apply the rule of exponents \(a^m / a^n = a^{m-n}\).

Simplify the expression \(\frac{8x^2y^2}{4x^2y^6}\).

Learn how to simplify the expression \(\frac{8x^2y^2}{4x^2y^6}\) using exponent rules and division of powers. This problem covers key algebraic concepts, suitable for students in Grades 7-9.

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